Dynamic Nuclear Polarization in Solid State NMR

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool in elucidating molecular structure and dynamics. It is applied in many areas of science and in medical imaging. In recent decades, magic angle spinning (MAS) solid state NMR (ssNMR) has developed into the method of choice for studying complex materials and biological systems in the solid state. Despite rapid advances in the field, applications in NMR are often limited by low sensitivity. One reason for this is the inherently low NMR transition energy and the associated Boltzmann population difference between nuclear spin states. Additionally, many MAS NMR experiments involve the direct detection of 13C and 15N and as such, isotopic labeling of these low abundance NMR active heteronuclei are often required [1].

Tremendous efforts have been made to improve NMR signal sensitivity. One approach is to employ hyperpolarization to induce a nuclear spin population difference far greater than that of the thermal equilibrium distribution. Dynamic nuclear polarization (DNP) is a technique where such hyperpolarization is achieved by the transfer of polarization from highly polarized electrons to the nuclei. The technique utilizes the larger population difference in spin states of the electrons in a magnetic field. This is approximately 660 times that of the population difference observed for protons as given by the ratio γe/γn, where γe and γn are the gyromagnetic ratio of the electron and the nucleus, respectively [2]. In practice, an enhancement (ε) in signal-to-noise ratio (S/N) of 40-200 have been observed.
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The concept of DNP was first introduced by Overhauser, then experimentally verified by Carver and Slichter for conducting solid metals and subsequently for solutions [3-5]. DNP has gained wide applicability in ssNMR given the larger enhancement which can be obtained and the often requirement for samples to be present at cryogenic temperatures. In a DNP experiment, the sample is doped with a paramagnetic agent which supplies a source of unpaired electrons. Microwave irradiation of the sample at the appropriate electron paramagnetic resonance (EPR) frequencies leads to the transfer of polarization to the bulk nuclear spins and results in DNP enhancement [2]. A brief discussion of the mechanisms of DNP is given in the next section, followed by an overview of instrumentation, sample preparation, and experimental setup. The paper concludes with a case study using the membrane protein bacteriorhodopsin and demonstrates the utility of DNP MAS NMR in studying complex biological systems.

Mechanisms of DNP​

For dielectric solids in a high magnetic field at low temperatures, DNP occurs via two principal mechanisms: the solid effect (SE) and the cross effect (CE). The relative importance of each pathway depends on the relationship between the nuclear Larmor frequency (ωn) and the EPR spectrum of the given paramagnetic species. Specifically, the SE pathway dominates if both the homogeneous linewidth (δ) and the inhomogeneous breath (Δ) of the EPR spectrum are smaller than ωn. When Δ > ωn > δ, CE becomes the major pathway [1]. Irradiation at specific frequencies may preferentially activate SE or CE, leading to DNP enhancement.

Solid Effect

The SE utilizes the dipolar coupling interactions between electron and nuclear spins [6]. The process depends on the mixing of the electronic and nuclear spin states and can be illustrated using a two-spin model described by a four-level energy diagram (Fig. 1) [1]. At thermal equilibrium, a very small population difference can be obtained at the NMR transitions. Irradiation is applied at the partially allowed double quantum (DQ, |--⟩ ⟷ |++⟩) or zero quantum (ZQ, |-+⟩ ⟷ |+-⟩) transition frequencies (ωe - ωn and ωe + ωn respectively), leading to saturation and equalized populations of the irradiated states. Consequently, the population difference corresponding to the NMR transitions becomes considerably larger and produces either a positive (double quantum) or a negative (zero quantum) signal enhancement in the NMR spectrum (Fig. 2).

At thermal equilibrium, a very small population difference can be obtained at the NMR transitions. Irradiation is applied at the partially allowed double quantum (DQ, |--⟩ ⟷ |++⟩) or zero quantum (ZQ, |-+⟩ ⟷ |+-⟩) transition frequencies (ωe - ωn and ωe + ωn respectively), leading to saturation and equalized populations of the irradiated states. Consequently, the population difference corresponding to the NMR transitions becomes considerably larger and produces either a positive (double quantum) or a negative (zero quantum) signal enhancement in the NMR spectrum (Fig. 2).

Figure 1. Energy level diagram of a two-spin model illustrating the SE. S and I denote the electron and the nuclear spin state, respectively. The relative population of spins occupying each energy level is represented by the size of the red spheres. Microwave irradiation at the DQ and ZQ transitions results in positive and negative DNP enhancement, respectively. Figure obtained and modified from Ni et al.[1]. 

Figure 2. DNP enhancement profile of the urea 1H NMR signal at incrementing magnetic fields under fixed 140 GHz microwave irradiation. Negative and positive DNP enhancements take place when the ZQ and DQ transitions are brought to match that of the microwave irradiation. Figure obtained and modified from Corzilius et al. [7]. 

The efficiency of the solid effect is influenced by a number of experimental parameters according to the following expression:

Where B1e is the magnetic field generated by the microwave power, B0 is the static magnetic field, Ne is the number of electrons, and T1n is the nuclear spin-lattice relaxation time [2]. The SE has an inverse squared dependence on B0 and is therefore less effective at higher magnetic fields. This is partially due to the inefficiency at exciting the electrons, in addition to the unfavorable mixing of electronic and nuclear spin states at higher fields [7]. Nevertheless, appreciable SE-induced DNP enhancement have been achieved using a suitable polarizing agent with higher microwave powers (Fig. 2) [7].

Cross Effect

The CE involves two coupled electrons, and a nucleus hyperfine-coupled to the electron pair [2]. Fig. 3 illustrates this three-spin model with an eight-energy level diagram where |SSI⟩ denotes the mixed spin state of the two electrons and the nucleus. If |ωe1 – ωe2| ≈ ωn, the two states |-++⟩ and |+--⟩ become degenerate. Irradiation at ωe1 or ωe2 would consequently saturate all four connected levels, leading to maximal DNP enhancement [1]. The CE is affected by several parameters per the equation below. Contrary to the SE, the CE scales proportionally to B0 and (Ne)^2 Therefore, it is more efficient at high fields and high radical concentrations relative to SE.

Figure 3. Energy level diagram of a three-spin model illustrating the CE. S and I denote the electron and the nuclear spin state, respectively. The relative population of spins occupying each energy level is represented by the size of the red spheres. When |ωe1 – ωe2| ≈ ωn, microwave irradiation ωe1 or ωe2 results in optimum positive and negative DNP enhancement, respectively. Figure obtained and modified from Ni et al.[1]. 

Spin Diffusion and Polarization Buildup

During DNP, electron polarization is first transferred to the core nuclei (nuclei which are hyperfine-coupled to the electrons) and gets subsequently transferred to the bulk nuclei (nuclei which are further away from the electrons and therefore do not exhibit hyperfine coupling). This process is mediated by spin diffusion, the exchange of magnetization between dipolar-coupled core and bulk nuclear spins [8]. In general, DNP-enhanced NMR signals are only observable for the bulk nuclei, while signals from the core nuclei are broadened beyond detection by their strong hyperfine coupling with electrons. In the case of proteins embedded in a solvent matrix, polarization transfer from the bulk nuclei to the protein of interest is required via spin diffusion [8].

Typically, an exponential polarization buildup is observed. The polarization buildup time is dependent on the microwave power, the gyromagnetic ratio of the electron and the nuclei, the concentration of the electrons and the nuclei, and relaxation rates. These factors affect the initial electron-nuclear polarization transfer, as well as spin diffusion to the bulk nuclei or nuclei at the site of interest [2]. For a protein sample, polarization buildup times of ~1 s, ~10 s, and ~260 s were observed for protons, carbons, and nitrogens, respectively. These differences could result from variations in the rate and the efficiency of spin diffusion, or from differences in nuclear relaxation times [2].

Instrumentation

Initially, DNP NMR experiments were conducted at low magnetic fields given the inverse relationships between ε and B0 and a lack of high power microwave source to excite the sub-terahertz EPR transitions under high fields [9]. Since then, sophisticated instrumentations have been developed to perform high frequency DNP NMR using contemporary high field magnets. The resulting improvements in spectral quality and resolution enabled researchers to interrogate increasingly complex systems that are otherwise unfeasible to study under low field conditions [9-11]. 

Microwave Source

Modern DNP experiments involve the coupling of NMR to a high power (>10W), high frequency (100-600 GHz) microwave source [2]. The latter is currently best achieved with a gyrotron-a fast-wave electron cyclotron maser whose resonance cavity is larger than its operating wavelength and therefore capable of generating high powers of continuous wave for an extended period of time. A custom-built DNP NMR system constructed by Bajaj et al. [9] is pictured in Fig 4. The 9 T (380 MHz) NMR magnet is connected to a 250 GHz gyrotron via a corrugated waveguide, through which microwaves are transmitted to the probe and the sample. The forward and reverse power are sampled by a directional coupler, providing feedback control of the gyrotron output power during an experiment. In this work, the system was continuously operated for 21 days with a power stability of <1% and a frequency stability of <400 kHz (1.6 ppm).

Figure 4. Top: schematic representation of a DNP NMR system. (1) 250 GHz gyrotron; (2) corrugated waveguide; (3) beam splitter; (4) forward power detector; (5) reflected power detector; (6) focusing and reflecting mirror optics; (7) helically corrugated waveguide; (8) miter mirror. Bottom: photograph of the setup. The 250 GHz gyrotron on the left is connected to the 380 MHz NMR on the right through a corrugated waveguide. Figure obtained from Bajaj et al. [9]. 

Cryogenic Probes

DNP NMR experiments require special probes that can operate at cryogenic temperatures, deliver microwaves, and detect NMR signals. The probe head for a solid-state DNP MAS NMR is depicted in Fig. 5. A sapphire rotor, transparent to high frequency microwaves, houses the NMR sample. Microwave power is directed through a corrugated waveguide, coaxial to the RF transmission line, and focused via a metal-mirror miter bend. Irradiation is applied perpendicular to the rotor axis, which is routinely spun at 10 kHz down to a temperature of 85 K using cryogenic nitrogen as the bearing and turbine gas [12].

Figure 5. Illustration of a DNP MAS ssNMR probehead. (1) stator; (2) sample rotor at the magic angle within the RF coil; (3) metal mirror miter bend; (4) inner conductor of the coaxial RF transmission line which serves as a corrugated waveguide; (5) Outer conductor of the RF line. Figure obtained from Barnes et al. [12]. 

Sample Preparation

Sample preparation is critically important for achieving high DNP enhancement, maintaining spectral resolution, and preserving sample integrity under cryogenic temperatures. The type and concentration of the polarizing agent should be carefully chosen. In addition, deuteration of the sample or the solvent should be considered.

Polarizing Agents

Diverse polarizing agents have been developed to increase DNP enhancement through maximizing the SE and the CE mechanisms. The structure of several commonly used polarizing agents are shown in Fig. 6. Trityl type radicals [13] and BDPA [14] (bis-α,γ-diphenylene-β-phenyl-allyl) with its water-soluble derivatives [15] rely on the SE pathway. These molecules exhibit narrow EPR spectra due to their three-fold molecular symmetry. Thus, frequency overlap between the DQ and the ZQ transitions are minimized, avoiding potential cancellation between the positive and the negative DNP enhancements.

Polarization transfer via CE, the dominant DNP pathway in high fields, requires a specific EPR frequency separation between two electrons in a three-spin system. To this end, biradical paramagnetic agents (molecules containing two unpaired electrons) were developed to improve electron-electron coupling and frequency matching. TEMPO (2,2,6,6-tetramethyl-piperidine-1-oxyls) is a commonly used nitroxide monoradical. By linking two TEMPO molecules through variable linkers, many biradicals were synthesized and tested [16-18]. BT2E (bis-TEMPO-2-ethylene oxide) and TOTAPOL (1-(TEMPO-4-oxy)-3-(TEMPO-4-amino)propan-2-ol) are each composed of two TEMPO moieties separated by a flexible linker (Fig. 6). Electron-electron coupling was significantly improved due to the shortened inter-electron distances (~13 Å), yielding larger DNP enhancements (in comparison to TEMPO) at higher magnetic fields and lower radical concentrations [16].

Through EPR line shape analysis, Hu et al. model the structure of several biradicals and the relative orientation of the g-tensors of the two TEMPO moieties. While the structure of TOTAPOL appears flexible, the g-tensors of its two TEMPO moieties are mostly perpendicular to each other. This yielded a EPR frequency separation which satisfies the CE matching condition. Based on this geometry, the biradical bTbk (bis-TEMPO-bisketal) was synthesized with a rigid bisketal linker in between two TEMPO moieties, restraining their g-tensors in a perpendicular orientation [17]. Despite its lower solubility, a larger DNP enhancement was observed for bTbk than for TOTAPOL under similar conditions.

​Figure 6. Structures of common DNP polarizing agents.

Radical Concentration

Paramagnetic effects, such as paramagnetic relaxation enhancement (PRE) and paramagnetic shifts, are functions of the radical concentration. The effect of radical concentration on DNP enhancement was investigated by Lange et al. using uniformly 13C-, 15N-labeled proline and various concentrations of TOTAPOL. As radical concentration increases, nuclear relaxation times T1 and T2* shorten appreciably due to PRE. The spin-lattice relaxation in the rotating frame (T1ρ) was also reduced at large radical concentration, leading to a drop in heteronuclear cross-polarization efficiency. Ultimately, DNP enhancement depends on the combined effects from these relaxation pathways. The decrease in T1 allows for shorter repetition delays and therefore an increase in S/N per unit time. On the other hand, a decrease in T2*, along with paramagnetic shift effects, cause line broadening. Using a constant experiment time and recycle delays optimized for individual samples, Lange et al. observed the signal enhancement to approach a maximum at 26 mM TOTAPOL, then dropping with further increase in radical concentration. The “bleaching effect” was modeled which yielded a rod-shaped volume, originating ~9-10 Å from the radical, within which no NMR signal is observe due to hyperfine coupling and paramagnetic relaxation effects. It was estimated that only ~50% of the nuclei are observable in a proline solution in the presence of 50 mM TOTAPOL [19]. Hence, radical concentration should be carefully controlled, and a lower radical concentration is often desirable.

Solvent and Sample Deuteration

DNP-enhanced NMR of solids are often performed at cryogenic temperatures to slow down the nuclear and electronic relaxation processes. Consequently, a cryoprotecting glass-forming solvent is required to uniformly distribute the radical and the analyte and prevent ice crystal formation [2]. Deuterated solvents are often used, such as d6-DMSO or a mixture of 60% d8-glycerol, 30% D2O, 10% H2O for protein samples. While the presence of protons facilitates spin diffusion and polarization transfer, a diluted proton concentration in deuterated solvents reduces unfavorable relaxation and results in better DNP enhancement.

Protein deuteration can also improve DNP enhancement. An increase in factors of roughly 4 and 19 were observed for protons and carbons, respectively, upon deuteration of the protein SH3 in comparison to the fully protonated SH3 [20]. The 13C DNP spectra of deuterated and protonated SH3 is compared in Fig. 7. In addition to the obvious rise in S/N as a result of deuteration, a further increase in signal intensity was observed with direct excitation of 13C compared to indirect detection through polarization transfer. The advances in sample preparation techniques, such as the development of better polarizing agents and sample deuteration, have enabled “high-temperature DNP” experiments (>100 K) while maintaining sufficient DNP enhancement [21]. Higher temperature often results in improved resolution and narrower linewidths, which is especially important for 2D and 3D NMR studies of complex biological systems [2]. The ability to conduct DNP experiments at variable temperatures greatly expanded the utility of DNP-ssNMR.

Figure 7. Comparison of the 13C NMR spectra of protonated and deuterated SH3. Figure obtained and modified from Akbey et al. [20]. 

Conclusion

DNP is a useful technique ssNMR. The signal enhancement depends on many factors including the type of polarizing agent, radical concentration, solvent and sample deuteration, and the instrumentation that is available. The development of high temperature and high frequency DNP allowed for better resolution and the study of complex biological systems. With continued improvements in gyrotron and probe technology, DNP can now be applied at even higher fields, up to 700 MHz [22]. The methodology is expected to greatly expand the utility and range of applications for ssNMR.

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